Question Video: Simplifying Quotients of Fractions Containing Monomials

Video Transcript

Consider the expression three 𝑥 cubed 𝑦 over five 𝑥𝑦 divided by six 𝑥 to the power of four over five 𝑦 to the power of four.

It is often easier to rewrite the expression using the division symbol as follows: three 𝑥 cubed 𝑦 divided by five 𝑥𝑦 divided by six 𝑥 to the power of four divided by five 𝑦 to the power of four. Then, we can rewrite the expression using the multiplication symbol: three 𝑥 cubed 𝑦 divided by five 𝑥𝑦 multiplied by five 𝑦 to the power of four divided by six 𝑥 to the power of four.

Now, use this form to help you simplify the original expression. There are two ways of approaching this problem. We could cancel or simplify first and then multiply the two fractions or we could multiply the two fractions and simplify this single fraction. We’re going to use the second method.

Multiplying the two numerators gives us 15𝑥 cubed 𝑦 to the power of five as three 𝑥 cubed 𝑦 multiplied by five 𝑦 to the power of four is equal to 15𝑥 cubed 𝑦 to the power of five. In the same way, multiplying the denominators, five 𝑥𝑦 multiplied by six 𝑥 to the power of four, gives us 30𝑥 to the power of five 𝑦.

We can then cancel or simplify this expression. 15 divided by 30 is equal to a half. 𝑥 cubed divided by 𝑥 to the power of five leaves us 𝑥 squared on the denominator. And 𝑦 to the power of five divided by 𝑦 is 𝑦 to the power of four.

Therefore, the simplified expression is 𝑦 to the power of four divided by two 𝑥 squared. Rewriting the initial expression has made it easier to simplify.